Question

integration of sec^2/3x.cosec^4/3x dx

Answer 1

integral sec^(2/3)(x) csc^(4/3)(x) x dx = (9 cos^2(x)^(1/3) sec(x) 2F1(1/3, 1/3, 4/3, sin^2(x)) - 6 x csc(x))/(2 csc^(2/3)(x) sec(x)^(1/3)) + constant

where F is a hypergeometric function